Will you please work #20 in section 4, Test 1.
Sure! When you see percents, you should almost always think about plugging in 100. In this case, that works like a charm. Say the laptop originally cost $100. When it was put on sale for 20% off, the price went to $80. Buying an $80 laptop with 8% sales tax will cost . Which answer choice gives you 100 when you plug in 86.4 for p? Only choice D.
If you want to know WHY that works, then look at the algebra. Forget about the tax for a moment. Alma bought the computer at a 20% discount. So if the computer originally cost x dollars, then the price she paid can be calculated thusly:
Now we need to add 8% sales tax to that. We do that by taking the price she paid and increasing it by 8%:
That expression gives you the price Alma paid for the laptop—which the question calls p. So we can say:
Since the question asks you for the original price, x, in terms of p, solve for x by dividing.
Choice D is correct, not choice C, according to the official book
Yes–that’s true. I rushed this a bit and misread the question. I was treating p like it’s the original price, but p is the actual amount Alma paid. I will update the post to reflect the correct solution.
How can p=0.8x+(0.08)(0.8x) be rewritten as p=1.08(0.8x)
Think of it like this. Replace 0.8x with A. Then you’ve got A + (0.08)A.
A + 0.08A
1A + 0.08A
Then just substitute 0.8x back in for A.